MinT - Best Known (205−59, 205, s)-Nets in Base 2

Best Known (205−59, 205, s)-Nets in Base 2

(205−59, 205, 135)-Net over F₂ — Constructive and digital

Digital (146, 205, 135)-net over F₂, using

2¹ times duplication [i] based on digital (145, 204, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 68, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(205−59, 205, 201)-Net over F₂ — Digital

Digital (146, 205, 201)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−59, 205, 1487)-Net in Base 2 — Upper bound on s

There is no (146, 205, 1488)-net in base 2, because

1 times m-reduction [i] would yield (146, 204, 1488)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 897813 420439 567426 461309 767002 261723 429105 385092 449296 122004 > 2²⁰⁴ [i]